Recently, with the remarkable development of a semiconductor laser, a Charge Coupled Device (CCD) and a Liquid Crystal Display (LCD), research on a holographic digital data storage has been actively conducted everywhere. In a holographic system, interference patterns generated when signal light derived from an object and reference light interfere with each other are recorded in a hologram storage medium. For example, such a storage medium includes photorefractive crystal sensitively reacting to the amplitude of the interference patterns. By varying an incident angle of the reference light on the hologram storage medium, the holographic system is capable of recording the amplitude and phase of signal light, thus displaying a three-dimensional image of an object, and storing several hundred to several thousand of holograms on a single storage medium.
In a recording mode of the holographic system, laser light generated from a light source is divided into reference light and object light. The reference light is reflected at a preset deflection angle and then generated in the form of reference light for recording to be incident on the hologram storage medium. The object light is modulated into signal light representing page image of binary input data to be recorded on the hologram storage medium. The modulated signal light and the reference light interfere with each other to generate an interference pattern. An image of the interference pattern is then recorded on the storage medium as hologram data corresponding to the binary input data. The hologram data to be recorded has a size of N×N pixels (for example, a size of 240×240 pixels) and is subject to a series of pre-processing processes (for example, an insertion of an error correction code (e.g., parity code) therein and a border generation for over-sampling, and then is modulated into the signal light through a SLM (a spatial light modulator) before being stored in the storage medium.
In a reproduction mode of the holographic system, an interference pattern recorded on the storage medium is converted into a page image through the use of an imaging device such as a CCD in a manner that a pixel in the SLM is mapped into 3×3 pixels in the CCD. For example, FIG. 6a illustrates an exemplary page image having a 1024×1024 pixel size reproduced from the storage medium and represented through the CCD. Such page image includes a data image with a size of 720×720 pixels and 3-pixel-sized upper, lower, left and right borders surrounding the data image.
In order to obtain an original data image with a size of N×N pixels, i.e., 240×240 pixels, it is needed to perform an over-sampling process wherein one pixel is extracted and then two pixels are skipped from the data image having a resolution size of 720×720 (i.e., a center pixel is extracted from each of 3×3 masks). FIG. 6b illustrates an exemplary data image having a 240×240 pixel size extracted by way of performing the over-sampling for the page image shown in FIG. 6a. 
For this end, it is necessary to detect the borders, thereby to define the data image. One of methods of detecting the borders is to obtain the sum of pixels arranged on each row line in the page image and the sum of pixel values arranged on each column line in the page image, each pixel has a binary value to represent pixel brightness.
FIG. 7 is an exemplary histogram showing the results of obtaining the sums of pixels arranged on each column line in the page image, wherein X-axis denotes column locations of pixels and Y-axis denotes pixel sums. As known from FIG. 7, there are two relatively higher sums (indicated by circles), on Y-axis, that are placed on two opposite sides on X-axis in the histogram. Coordinates on X-axis corresponding to the two relatively higher sums represent locations of left and right borders. The reason that the sum of pixels at the borders is relatively high is because pixels forming the borders have the same binary value of approximately “1”, instead that pixels having value of “1” or “0” randomly exist together in the data image. In FIG. 7, the left border corresponds to a 140-th pixel location, and the right border corresponds to a 877-th pixel location. In this case, a region of the left border occupies eight pixels ranging from a 140-th pixel to a 147-th pixel.
After detecting the locations of the borders as described above, each center pixel is extracted for three pixels using the over-sampling process while sequentially moving a mask from an upper left corner to an upper right corner in the data image surrounded by the borders, as shown in FIGS. 8a and 8b. 
As described above, if the location of the left border is a 140-th pixel, a theoretical location of the right border should be an 875-th pixel. However, an actual location of the right border is an 877-th pixel as indicated in FIG. 7, which means that there is a magnification of 2 pixels in comparison to the theoretical result.
Thus, in order to compensate distortions of the magnified pixels, the prior art divides an entire data image (i.e., every row and column line) into three equal portions, and performs over-sampling in such a way that three, instead of two, pixels are skipped only at the start positions of the second and third equal portions. For example, the over-sampling process is performed to skip for every two pixels in the data image having 720×720 pixel and to skip three pixels at locations of 389-th pixel and 630-th pixel which correspond to ⅓ division and ⅔ division from the 140-th pixel to the 877-th pixel. As a result, it is possible to achieve compensation of distortions in the data image on a pixel-by-pixel basis.
However, since the locations of the borders are measured on a pixel basis, it is impossible to precisely compensate the distortion on a half-pixel basis, which causes a problem in that a high quality data image cannot be obtained.